Vertically and horizontally directed muscle power ...

RESEARCH ARTICLE

Vertically and horizontally directed muscle

power exercises: Relationships with top-level

sprint performance

Irineu Loturco1*, Bret Contreras2, Ronaldo Kobal1, Victor Fernandes3,4, Neilton Moura3,

Felipe Siqueira4,5, Ciro Winckler6, Timothy Suchomel7, Lucas Adriano Pereira1

1 NAR—Nucleus of High Performance in Sport, São Paulo, Brazil, 2 Auckland University of Technology,

Sport Performance Research Institute New Zealand, Auckland, New Zealand, 3 B3 Track & Field Club, São

Paulo, Brazil, 4 ADAPT—Association of High-Performance Training & Sports Development, São Paulo,

Brazil, 5 Pinheiros Sport Club, São Paulo, Brazil, 6 Brazilian Paralympic Committee, São Paulo, Brazil,

7 Department of Human Movement Sciences, Carroll University, Waukesha, WI, United States of America

* [email protected]

Abstract

The capacity to rapidly generate and apply a great amount of force seems to play a key role

in sprint running. However, it has recently been shown that, for sprinters, the technical ability

to effectively orient the force onto the ground is more important than its total amount. The

force-vector theory has been proposed to guide coaches in selecting the most adequate

exercises to comprehensively develop the neuromechanical qualities related to the distinct

phases of sprinting. This study aimed to compare the relationships between vertically-

directed (loaded and unloaded vertical jumps, and half-squat) and horizontally-directed (hip-

thrust) exercises and the sprint performance of top-level track and field athletes. Sixteen

sprinters and jumpers (including three Olympic athletes) executed vertical jumps, loaded

jump squats and hip-thrusts, and sprinting speed tests at 10-, 20-, 40-, 60-, 100-, and 150-

m. Results indicated that the hip-thrust is more associated with the maximum acceleration

phase (i.e., from zero to 10-m; r = 0.93), whereas the loaded and unloaded vertical jumps

seem to be more related to top-speed phases (i.e., distances superior to 40-m; r varying

from 0.88 to 0.96). These findings reinforce the mechanical concepts supporting the force-

vector theory, and provide coaches and sport scientists with valuable information about the

potential use and benefits of using vertically- or horizontally-based training exercises.

Introduction

The ability to rapidly generate and apply a substantial amount of force is recognized to play an

important role in top-level sprint performance [1]. Accordingly, several authors have reported

strong correlations between a wide spectrum of neuromechanical capacities and maximal

sprint velocity [2–4]. Moreover, numerous experimental studies have demonstrated that

increases in muscle power output result in meaningful improvements in speed, which could

confirm the casual relationship between these mechanical variables [5–7]. Nevertheless, it has

been shown that the technical ability to apply force effectively against the ground is more

important to elite sprint performance than its total amount [8].

PLOS ONE | https://doi.org/10.1371/journal.pone.0201475 July 26, 2018 1 / 13

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OPENACCESS

Citation: Loturco I, Contreras B, Kobal R,

Fernandes V, Moura N, Siqueira F, et al. (2018)

Vertically and horizontally directed muscle power

exercises: Relationships with top-level sprint

performance. PLoS ONE 13(7): e0201475. https://

doi.org/10.1371/journal.pone.0201475

Editor: Slavko Rogan, Berner Fachhochschule,

SWITZERLAND

Received: January 29, 2018

Accepted: July 16, 2018

Published: July 26, 2018

Copyright: © 2018 Loturco et al. This is an open

access article distributed under the terms of the

Creative Commons Attribution License, which

permits unrestricted use, distribution, and

reproduction in any medium, provided the original

author and source are credited.

Data Availability Statement: All relevant data are

within the paper.

Funding: The researchers Victor Fernandes,

Neilton Moura, Felipe Siqueira, and Ciro Winckler

of the study entitled: “Vertically and horizontally

directed muscle power exercises: relationships

with top-level sprint performance”, declare that

they have commercial affiliation with the following

funders: B3 Track & Field Club, São Paulo, Brazil;

ADAPT - Association of High-Performance Training

& Sports Development, São Paulo, Brazil; Pinheiros

https://doi.org/10.1371/journal.pone.0201475

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http://creativecommons.org/licenses/by/4.0/

Indeed, it seems that the capability to orient the resultant force vector horizontally while

accelerating is a key determinant of human speed [8,9]. Therefore, athletes able to produce

large amounts of forces onto the ground in the forward direction (i.e., horizontal plane) are

probably more prone to achieve greater velocities while sprinting. Briefly, the horizontal force

output appears to be more related to the maximum acceleration phases (e.g., from zero to

50-m), where contact times are longer and running velocities are lower than those found dur-

ing top-speed phases [10]. In contrast, it has been shown that the transition from lower to

higher velocities results in shorter support phase duration with concomitant increases in verti-

cal peak force [11,12]. That said, it is reasonable to assume that exercises performed in the ver-

tical or horizontal axis may present varied levels of relationships and interactions with distinct

phases of sprint running.

More recently, the force-vector theory has been proposed to guide coaches and researchers

in selecting the most appropriate exercises and drills for improving each specific phase of max-

imum running speed. For example, Contreras et al. [13] verified that the horizontally-oriented

hip-thrust is superior to the front squat to increase acceleration over 20-m after a short-term

intervention (i.e., 6-week), which is probably related to the anteroposterior force vector

employed in this movement and its potential impact on horizontal impulse production [14].

On the other hand, Kale et al. [15] demonstrated that, among several variables collected in ver-

tical and horizontal jumps, the drop jump height is the best indicator of maximum velocity

attained by an elite sprinter throughout a 100-m dash race. Similar results were obtained in a

series of recent investigations executed with sprinters and team sport athletes, confirming that

the direction of the resistance force vector relative to the body is determinant in mediating

adaptations to speed qualities [4,16,17]. However, although some of these studies have been

carried out using vertical exercises performed at the optimum power zones (i.e., using loads

capable of maximizing power output) [4,16,18], there is a lack of research on this topic with

horizontally-directed exercises (e.g., hip-thrust).

Taking into consideration the apparent effectiveness of the optimum power zones [19,20],

it would appear important to test the relationships between hip-thrusts executed under opti-

mum loading conditions and the actual performance of top-level sprinters over a comprehen-

sive range of sprint distances (i.e., from zero to 150-m). Moreover, it would be relevant to

compare the predictive abilities of hip-thrusts and the widely used vertically-oriented exercises

(e.g., half-squat and vertical jumps) with respect to different phases of sprint running. These

inferences may help practitioners to develop better and more specific strategies to improve the

speed qualities of their athletes. The aim of this study was to examine the relationships between

several mechanical measures assessed in hip-thrusts and loaded jump squats (executed at their

respective optimum power zones), unloaded vertical jumps, and the performances obtained by

professional sprinters and jumpers in different sprint distances, varying from 10- to 150-m.

Based on previous data [4,13,16] and our extensive experience with these athletes, we expected

that better performances in the horizontally-oriented exercise (i.e., hip-thrust) would be

directly related to better results obtained during the initial phases of sprinting (from zero to

50-m), whereas the greatest outputs collected during vertically-oriented movements (i.e., half-

squats, loaded and unloaded vertical jumps) would be more associated with the highest veloci-

ties attained during the top-speed phases (i.e., distances� 40-m).

Materials and methods

Study design

This cross-sectional descriptive study aimed to examine the relationships between various neu-

romuscular tests and the sprint performance of elite track and field athletes in different

Vertically and horizontally directed exercises and sprint performance


Sport Club, São Paulo, Brazil; Brazilian Paralympic

Committee, São Paulo, Brazil. The funder provided

support in the form of salaries for authors VF, NM,

FS, CW, but did not have any additional role in the

study design, data collection and analysis, decision

to publish, or preparation of the manuscript. The

specific roles of these authors are articulated in the

’author contributions’ section. This does not alter

our adherence to PLOS ONE policies on sharing

data and materials.

Competing interests: The researchers Victor

Fernandes, Neilton Moura, Felipe Siqueira, and Ciro

Winckler, authors of the study entitled: “Vertically

and horizontally directed muscle power exercises:

relationships with top-level sprint performance”,

declare that they have commercial affiliation with

the following funders: B3 Track & Field Club, SãoPaulo, Brazil; ADAPT - Association of High-

Performance Training & Sports Development, SãoPaulo, Brazil; Pinheiros Sport Club, São Paulo,

Brazil; Brazilian Paralympic Committee, São Paulo,

Brazil. The authors recognize and certify that there

is no conflict of interest to declare. This

commercial affiliation does not alter our adherence

to PLOS ONE policies on sharing data and

materials.


running distances. To define these relationships, subjects executed the tests on two consecutive

days, in the following order: day 1) vertical jumps comprising squat and countermovement (SJ

and CMJ, respectively); a 60-m sprint; day 2) a 150-m sprint; and jump squat (JS), half-squat

(HS), and hip-thrust (HT) exercises assessing mean propulsive power outputs (MPP). After

the first day, athletes rested until the next day of assessments. During this period, they were

instructed to maintain their nutritional and sleep habits and to arrive at the sports laboratory

in a fasting state for at least 2-h, avoiding alcohol and caffeine consumption for at least 48-h

before the tests. All subjects were previously familiarized with the testing procedures due to

their constant assessments in our facilities. A standardized warm-up was performed before the

tests comprising light to moderate self-selected runs for 5-min. Sub-maximal attempts at each

test were also performed prior to the maximal tests. Between each test, a 15-min rest interval

was implemented to explain the next testing procedures and adjust the testing devices. All

physical tests were performed between 9:00 a.m. and 13:00 p.m.

Participants

Sixteen top-level sprinters and jumpers (9 men and 7 women; 21.8 ± 3.0 years; 177.7 ± 10.6

cm; 67.4 ± 10.8 kg) participated in this study. The sample comprised 3 athletes who partici-

pated in the last Olympic Games (Rio-2016), while the other participants have been involved

in World Championships, Pan-American, and South-American competitions, attesting their

high level of performance and competitiveness. Prior to participating in this study, athletes

were briefed on the experimental design and signed an informed consent form. The athletes in

this manuscript have given written informed consent, as outlined in PLOS consent form, to

publish this study. This study was performed in accordance with the ethical standards of the

Helsinki Declaration and was approved by the Anhanguera-Bandeirante University Ethics

Committee.

Vertical jumps

Vertical jump height was assessed using SJ and CMJ. In the SJ, athletes were required to

achieve a squat position with 90˚ of knee flexion and hold this position for ~2-s before jump-

ing, without any preparatory movement. In the CMJ, athletes were instructed to execute a

downward movement followed by complete extension of the hip, knee, and ankle joints and

were free to determine the countermovement amplitude to avoid changes in jumping coordi-

nation. All jumps were executed with the hands on the hips and the athletes were instructed to

jump as high as possible. The jumps were performed on a valid and reliable contact mat (Elite

Jump, S2 Sports, São Paulo, Brazil) [21]. The obtained flight time (t) was used to estimate the

jump height (h) (i.e., h = gt2/8), where “g” is the acceleration due to gravity. A total of five

attempts were allowed for each jump, interspersed by 15-s intervals. The best attempt at each

jump was used for the analyses.

Sprinting velocity

For the 60-m sprint test (day 1), five pairs of photocells (Smart Speed, Fusion Equipment, Bris-

bane, AUS) were positioned at distances of 0, 10-, 20-, 40-, and 60-m along the sprinting

course. Meanwhile, for the 150-m sprint test (day 2), three pairs of photocells were positioned

at distances of 0, 100-, and 150-m along the sprinting course. Athletes performed two 60-m

sprints and two 150-m sprints starting from a standing position 0.3 m behind the starting line.

The sprint tests were performed on an official running track. An 8-min rest interval was

allowed between the two attempts and the fastest time was considered for the analyses.




Mean propulsive power outputs

Mean propulsive power outputs (MPP) were measured in the JS and HS exercises, performed

on a Smith-Machine (Hammer Strength Equipment, Rosemont, IL, USA) and in the HT exer-

cise performed using an Olympic bar. The athletes were instructed to execute three repetitions

at maximal velocity for each load, with a 5-min interval provided between sets. The test started

at a load corresponding to 40% of the athlete’s body mass (BM). A load of 10% of BM for all

exercises was gradually added in each set until a clear decrement in the MPP was observed. In

the JS (Fig 1), the athletes squatted until the tops of their thighs were parallel to the ground

and, after a verbal command, jumped as fast as possible without their shoulder losing contact

with the barbell. The HS was executed in a similar fashion to the JS, except that the subjects

were instructed to move the bar as fast as possible without losing foot contact with the ground.

For the HT (Fig 2), athletes positioned their upper backs on a bench with the barbell placed

over the hips [13]. Subjects were instructed to thrust the bar upwards as fast as possible, while

maintaining a neutral spine and pelvis. To determine MPP outputs, a linear transducer

(T-Force, Dynamic Measurement System; Ergotech Consulting S.L., Murcia, Spain) was

attached to the Smith-Machine bar [4,22,23]. The bar position data were sampled at 1,000 Hz

using a computer. The finite differentiation technique was used to calculate bar-velocity and

acceleration. The maximum MPP obtained and the mean propulsive velocity (MPV) associ-

ated with the maximum MPP in each exercise were used for analysis.

Statistical analysis

Data are presented as means ± standard deviation. The normality of data was tested using the

Shapiro-Wilk test. Pearson product-moment coefficient of correlation was used to determine

the relationships between the performances in the sprinting velocities with the vertical jumps

and the MPP in the HS, JS, and HT exercises. The threshold used to qualitatively assess the cor-

relations was based on the following criteria: <0.1, trivial; 0.1–0.3, small; 0.3–0.5, moderate;

0.5–0.7, large; 0.7–0.9, very large; >0.9 nearly perfect [24]. To better determine the predictive

ability of the assessed exercises in relation to the different sprint distances analyzed, data are

expressed as shared variance (R2). The level of significance was set at P< 0.05. The analyses

were performed using IBM SPSS Statistics for Windows, Version 20.0 (IBM Corp., Armonk,

NY, USA). The magnitude of the differences between two significant correlations was assessed

using the effect size (ES) analysis [25]. The magnitudes of the ES were qualitatively interpreted

using the following thresholds: <0.10, trivial; 0.10–0.30 small; 0.30–0.50 moderate;>0.50,

large [25]. All performance tests presented good levels of absolute and relative reliability

(CV< 5% and ICC > 0.90 for all assessments) [24].

Results

Table 1 shows the descriptive data of the performances in the vertical jumps, MPP in the differ-

ent exercises, and sprinting velocities for the top-level sprinters and jumpers. Fig 3 depicts the

dynamics of the correlations between sprinting velocities across the different distances tested

with the vertical jumps and the MPP in the three different exercise tests. Table 2 shows the

shared variance (R2) of the relationships among the sprint velocities and the vertical jumps

and power measures. Table 3 shows the mean differences, 95% confidence intervals, and effect

sizes for the comparisons between the significant correlations. Table 4 demonstrates the mean

MPV values and the between subject coefficient of variation (CV) associated with the maxi-

mum MPP for each exercise tested.







Discussion

This study examined the relationships of vertically- and horizontally-directed muscle power

exercises and the actual performance of professional track and field athletes in distances vary-

ing from 10- to 150-m. The main finding reported here is that, independent of the movement

axis (vertical or horizontal), all assessed exercises presented very large to nearly perfect correla-

tions with all sprint distances (i.e., 10-, 20-, 40-, 60-, 100-, 150-m). Notably, the horizontally-

oriented HT showed stronger associations with the initial phase of sprinting (from zero to

10-m), whereas the unloaded vertical jumps appeared to be more related with longer sprint

distances (100-m), and consequently higher running velocities. To our knowledge, this is the

first investigation to document the possible role played by the force-vector theory on the

mechanical relationships that exist between certain vertical and horizontal strength-power

exercises and the performance obtained by top-level sprinters and jumpers over a comprehen-

sive distance of 150-m.

Although small, the differences between the correlations presented by hip-thrust and verti-

cal jumps in the maximum acceleration phase (i.e., from zero to 10-m) should be highlighted

and considered as worthwhile outcomes (Table 3). Indeed, in elite sprinting, trivial variances

Fig 1. A Pan-American champion (sprinter) performing a loaded jump squat at the optimum power zone.

https://doi.org/10.1371/journal.pone.0201475.g001

Fig 2. An Olympic sprinter performing a loaded hip-thrust at the optimum power zone.







in time may represent meaningful and decisive differences in competitive performance [26];

therefore, track and field coaches are frequently obliged to select the most effective strategies

to improve all speed qualities related to running speed [27]. In this sense, the nearly perfect

associations found between HT MPP and all velocities assessed within the acceleration phase

(up to 60-m) represent an important input for the development of optimal sprint training

interventions. Previous studies have demonstrated that horizontally-directed exercises

increased sprint speed over very short distances in adolescent athletes and soccer players

[13,17]. However, Bishop et al. [28] indicated that training with the HT exercise twice per

week for eight weeks did not improve 0-10-, 10-20-, 20-30-, 30-40-, or 40-m sprint time in

male and female collegiate athletes. The data in the current study support the use of the HT

exercise for developing maximum acceleration capacity in top-level sprinters; nevertheless,

due to the conflicting results regarding its potential long-term training benefits, further

research is needed to determine the chronic effectiveness of the HT exercise in this population.

Interestingly, despite its vertical orientation, the HS power measures showed nearly perfect

correlations with 10-m velocity. From a mechanical standpoint, this can be explained when

analyzing the force-velocity relationship in traditional (non-ballistic) and ballistic exercises. It

is worth noting that, with the exception of the unloaded jumps, all movements assessed in this

research were performed with the load capable of maximizing power output. At these zones

(which can be easily identified by instantaneously measuring the bar-velocity; Table 4), tradi-

tional exercises (e.g., HS) are favoured by heavy-loading, low-velocity conditions, whereas

more rapid movements (e.g., JS) are favoured by light-loading, high-velocity conditions

[29,30]. It is rational to consider that sprinters able to produce higher levels of muscle power at

lower velocities would be equally effective to overcome the inertia during the initial phases of

sprinting, accelerating their bodies forward in an efficient manner [4,8,9]. As an additional

point, it is crucial to observe that the remaining loaded exercises (i.e., JS and HT) presented

similar correlation magnitudes with sprint performance throughout the entire 150-m course.

These findings reinforce the previous evidence indicating that the optimum power zone might

be an effective and useful range of loads to assess and train top-level athletes, mainly those who

need to develop their speed-related capacities [18,19].

Similar mechanical factors may also explain the specific trends of the correlations presented

by unloaded vertical jumps across all sprint distances (from 10- to 150-m). As aforementioned,

Table 1. Mean ± standard deviation (SD) of the vertical jumps, maximum mean propulsive power (MPP) in the

different exercises, and sprinting velocities for the different distances tested in top-level sprinters and jumpers.

Mean ± SD 90% Confidence limits

Lower Upper

SJ (cm) 48.4 ± 8.6 44.2 51.9

CMJ (cm) 51.7 ± 9.3 47.2 55.6

MPP HS (W) 805.1 ± 223.3 681.2 907.1

MPP JS (W) 1020.0 ± 317.0 841.2 1157.6

MPP HT (W) 950.0 ± 274.0 826.9 1102.9

VEL 10-m (m.s-1) 5.99 ± 0.33 5.83 6.15

VEL 20-m (m.s-1) 6.99 ± 0.37 6.80 7.18

VEL 40-m (m.s-1) 7.97 ± 0.51 7.74 8.25

VEL 60-m (m.s-1) 8.45 ± 0.60 8.17 8.77

VEL 100-m (m.s-1) 8.64 ± 0.68 8.36 9.03

VEL 150-m (m.s-1) 8.66 ± 0.77 8.34 9.10

Note:SJ: squat jump, CMJ: countermovement jump; HS: half-squat; JS: jump squat; HT: hip-thrust; VEL: velocity.

https://doi.org/10.1371/journal.pone.0201475.t001





whereas the horizontal force production has been more associated with maximum acceleration

performance, the vertical peak force seems to play an increasing and critical role during the

transition from lower to higher velocities [11,12]. From our data, it is possible to confirm this

Fig 3. Correlations (90% confidence limits) between sprinting velocities for the different distances tested with squat and countermovement jumps (SJ and CMJ),

and the mean propulsive power (MPP) in the half-squat (HS), jump squat (JS), and hip-thrust (HT) exercises. P< 0.05 for all correlation coefficients.






Table 2. Shared variance (R2) of the relationships among the sprint velocities and the vertical jumps and the maximum mean propulsive power (MPP) in the differ-

ent exercises in top-level sprinters and jumpers.

Sprint velocities

10-m 20-m 40-m 60-m 100-m 150-m

SJ 0.60 0.86 0.86 0.92 0.88 0.86

CMJ 0.60 0.85 0.90 0.86 0.86 0.81

MPP HS 0.82 0.93 0.91 0.87 0.76 0.74

MPP JS 0.75 0.90 0.92 0.89 0.79 0.77

MPP HT 0.86 0.91 0.91 0.89 0.72 0.74

Note:SJ: squat jump, CMJ: countermovement jump; HS: half-squat; JS: jump squat; HT: hip-thrust.


Table 3. Mean differences (± 95% confidence limits; CL) and effect sizes (ES) for the comparisons between significant correlations.

Sprint velocities

10-m 20-m 40-m 60-m 100-m 150-m

SJ-CMJ Mean dif. -0.01 0.01 -0.02 0.03 0.01 0.03

CL (-0.31; 0.29) (-0.18; 0.20) (-0.19; 0.15) (-0.13; 0.19) (-0.17; 0.19) (-0.17; 0.23)

ES -0.02 0.07 -0.17S 0.29S 0.08 0.19S

SJ-JS Mean dif. -0.09 -0.02 -0.03 0.02 0.05 0.05

CL (-0.36; 0.18) (-0.19; 0.15) (-0.20; 0.14) (-0.13; 0.17) (-0.15; 0.25) (-0.16; 0.26)

ES -0.31M -0.17S -0.29S 0.21S 0.32M 0.28S

SJ-HS Mean dif. -0.13 -0.03 -0.03 0.03 0.07 0.07

CL (-0.39; 0.13) (-0.19; 0.13) (-0.20; 0.14) (-0.13; 0.19) (-0.14; 0.28) (-0.15; 0.29)

ES -0.51L -0.29S -0.17S 0.29S 0.41M 0.37M

SJ-HT Mean dif. -0.15 -0.03 -0.03 0.02 0.09 0.07

CL (-0.40; 0.10) (-0.20; 0.14) (-0.20; 0.14) (-0.14; 0.18) (-0.13; 0.31) (-0.15; 0.29)

ES -0.64L -0.29S -0.29S 0.21S 0.48M 0.37M

CMJ-JS Mean dif. -0.09 -0.03 -0.01 -0.01 0.04 0.02

CL (-0.36; 0.18) (-0.21; 0.15) (-0.16; 0.14) (-0.18; 0.16) (-0.16; 0.24) (-0.20; 0.24)

ES -0.29S -0.24S -0.11S -0.08 0.24S 0.10S

CMJ-HS Mean dif. -0.13 -0.04 0.00 0.00 0.06 0.04

CL (-0.39; 0.13) (-0.22; 0.13) (-0.15; 0.15) (-0.18; 0.18) (-0.15; 0.27) (-0.19; 0.27)

ES -0.48M -0.36M 0.00 0.00 0.33M 0.18S

CMJ-HT Mean dif. -0.15 -0.04 -0.01 -0.01 0.08 0.04

CL (-0.40; 0.10) (-0.21; 0.13) (-0.16; 0.14) (-0.19; 0.17) (-0.14; 0.30) (-0.19; 0.27)

ES -0.61L -0.36M -0.11S -0.08 0.40M 0.18S

JS-HS Mean dif. -0.04 -0.01 0.01 0.01 0.02 0.02

CL (-0.27; 0.19) (-0.16; 0.14) (-0.14; 0.16) (-0.16; 0.18) (-0.21; 0.25) (-0.22; 0.26)

ES -0.20S -0.11S 0.11S 0.08 0.09 0.08

JS-HT Mean dif. -0.06 -0.01 0.00 0.00 0.04 0.02

CL (-0.28; 0.16) (-0.16; 0.14) (-0.15; 0.15) (-0.17; 0.17) (-0.20; 0.28) (-0.22; 0.26)

ES -0.33M -0.11S 0.00 0.00 0.17S 0.08

HS-HT Mean dif. -0.02 0.01 -0.01 -0.01 0.02 0.00

CL (-0.22; 0.18) (-0.13; 0.15) (-0.16; 0.14) (-0.18; 0.16) (-0.23; 0.27) (-0.25; 0.25)

ES -0.13S 0.00 -0.11S -0.08 0.08 0.00

Note: SJ: squat jump, CMJ: countermovement jump; HS: half-squat; JS: jump squat; HT: hip-thrust; S, M, and L represent small, moderate, and large effect sizes,

respectively.







theoretical perspective, after verifying that CMJ and SJ heights were the only variables that pre-

sented nearly perfect correlations in all distances equal or superior to 40-m (i.e., high-velocity

phases). Furthermore, the relationships between these unloaded vertical exercises and 10-m

velocity were the weakest (R2 = 0.60 for both jump types) among all the parameters analyzed

in this study, again supporting the original concepts proposed by the force-vector theory

[13,16]. Lastly, it should be emphasized that jump heights are measures able to express

mechanical values already corrected by the athlete’s body mass. As a consequence, if during a

vertical jump attempt a sprinter jumps higher, he necessarily produces superior values of rela-

tive force and power than his weaker peer, which is recognized to be of great importance for

achieving higher velocities while sprinting [2,4]. These results have a significant impact on

applied practice and research, since jump-based measurements may be considered as one of

the most practical and useful approaches for assessing elite athletes.

This study is limited by the cross-sectional nature of the dataset, which precludes the

extrapolation of our findings to causal inferences. Nonetheless, we examined the speed and

power performance of top-level track and field athletes, including Olympic athletes and Pan-

American Champions, who can be classified as individuals at the upper limits of human per-

formance. Although we acknowledge our inability to draw definitive conclusions about the

efficacy of these exercises, we consider that our findings provide valuable insight into the spe-

cific role played by vertically or horizontally-directed movements in the distinct phases of

sprint performance. This information will certainly help coaches and sport scientists to

develop better and more effective training programs for professional sprinters, in a particular

sport field where very small differences may represent a fine line between victory and defeat

[26].

Practical applications

The force-vector theory is an emergent methodological approach, based on a solid and well-

established mechanical foundation. Through the use of this concept, strength and condition-

ing specialists may select the resistance exercises more connected with the different phases of

sprint running, namely maximum acceleration and top-speed phases. Based on our results,

athletes with the primary objective of developing speed qualities more related to the initial

phases of sprinting may consider the use of horizontally-directed exercises, specifically the HT,

over the use of vertically-directed exercises. Alternatively, if the main training objective is to

improve the neuromechanical capacities consistently associated with higher sprint velocities,

implementation of loaded and unloaded vertical jumps during the resistance training sessions

seems to be an effective strategy. While the resistance training emphasis may shift towards

using horizontally-directed exercises when emphasizing the maximum acceleration phase, it

should be noted that vertically-directed exercises should not be eliminated from training pro-

grams, considering the later sprint phases and their significant relationships throughout the

different sprinting distances. For the same reason, horizontally-directed exercises must not be

Table 4. Mean ± standard deviation (SD), between subject coefficient of variation (CV), and 90% confidence lim-

its of the mean propulsive velocities (MPV) associated with the maximum mean propulsive power values in the

half-squat (HS), jump squat (JS), and hip-thrust (HT) exercises in top-level sprinters and jumpers.

Mean ± SD CV% 90% Confidence limits

Lower Upper

MPV HS (m.s-1) 0.84 ± 0.06 6.7 0.79 0.85

MPV JS (m.s-1) 1.04 ± 0.08 7.3 1.00 1.07

MPV HT (m.s-1) 1.03 ± 0.08 7.4 0.99 1.07






eliminated during maximal speed phases, while (in theory) vertically-directed exercises should

be prioritized. Thus, using a combination of both horizontally- and vertically-directed exer-

cises within resistance training programs is strongly recommended; however, the emphasis on

one or the other may be dependent on the speed development qualities sought. In addition to

these exercises, the traditional HS (usually performed with higher loads, at lower speeds) may

be used to enhance the ability to overcome the moment of inertia throughout the maximum

acceleration phase. Together, these data may help track and field coaches and researchers pro-

duce faster and more efficient athletes, in a sport discipline where very brief periods of time

such as hundredths of seconds can separate Olympic gold medalists from National competi-

tors. Further studies should be conducted to test the causal impact of the relationships reported

here and to compare the role played by the force-vector and force-velocity theories in elite

sprint performance.

Author Contributions

Conceptualization: Irineu Loturco, Bret Contreras, Victor Fernandes, Timothy Suchomel,

Lucas Adriano Pereira.

Data curation: Irineu Loturco, Ronaldo Kobal, Victor Fernandes, Neilton Moura, Felipe

Siqueira, Ciro Winckler, Lucas Adriano Pereira.

Formal analysis: Irineu Loturco, Bret Contreras, Ronaldo Kobal, Victor Fernandes, Neilton

Moura, Felipe Siqueira, Ciro Winckler, Timothy Suchomel, Lucas Adriano Pereira.

Investigation: Irineu Loturco, Ronaldo Kobal, Victor Fernandes.

Methodology: Irineu Loturco, Ronaldo Kobal, Victor Fernandes, Neilton Moura, Felipe

Siqueira, Ciro Winckler, Timothy Suchomel, Lucas Adriano Pereira.

Supervision: Irineu Loturco, Bret Contreras.

Writing – original draft: Irineu Loturco, Bret Contreras, Timothy Suchomel, Lucas Adriano

Pereira.

Writing – review & editing: Irineu Loturco, Bret Contreras, Ronaldo Kobal, Victor Fer-

nandes, Neilton Moura, Felipe Siqueira, Ciro Winckler, Timothy Suchomel, Lucas Adriano

Pereira.

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Vertically and horizontally directed muscle power ...

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